Mr Galloway wrote: “Dumbfounding. She calls Chomsky an anti-Semite and slanders half the Labour Party as the same.”
In response, Ms Riley tweeted: “F*** off George Galloway. Today is not the day I'm going to be polite to antisemite scum - to be explicit.”
Mr Galloway has been approached for comment.
In December, Ms Riley, who is Jewish, said she received a barrage of abuse after she shared a video by anti-racist campaigners that condemned antisemitism in football.
She shared a three-minute long video, which was developed by the football equality organisation Kick It Out and Chelsea football club.
But after sharing the video, which showed how antisemitic abuse is still prevalent in English football, she said she was “inevitably confronted with weird and aggressive posts about Israel and Zionists”.
Since then, she has used her Twitter profile to raise concerns about antisemitism she had received and seen elsewhere.
She thanked other high profile Twitter users for standing with her.
Her colleague and Countdown host Nick Hewer has spoken out in support for her.
Mr Hewer, a long time Labour voter, said he will no longer vote for the party in protest against the abuse suffered his by colleague.
Stephen Fry also tweeted to her on Thursday: “I stand with you”.
Ms Riley has tweeted to thank those “standing shoulder to shoulder with me and so many others, against bullying, and against antisemitism. It's so very much appreciated.”
